Completeness of coalition logics with seriality, independence of agents, or determinism

2024-09-23

arXiv.org

AI Summary

This paper addresses the strong completeness problem for Coalition Logic under three classical assumptions—sequentiality, agent independence, and determinism. We propose the first unified proof framework, departing from prior approaches that require ad hoc semantic model constructions for each assumption combination. Our method builds upon general concurrent game models and integrates canonical model construction, filtration techniques, and modal semantic adaptation to achieve modular and extensible verification. We rigorously establish strong completeness for nine distinct Coalition Logic systems—covering all single-assumption, double-assumption, and full-assumption combinations. This result bridges the formal gap between minimal Coalition Logic and realistic strategic reasoning scenarios, thereby providing a robust logical foundation for modeling strategic capability in multi-agent systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

Coalition Logic is a central logic in logical research on strategic reasoning. In a recent paper, Li and Ju argued that generally, models of Coalition Logic, concurrent game models, have three too strong assumptions: seriality, independence of agents, and determinism. They presented a Minimal Coalition Logic based on general concurrent game models, which do not have the three assumptions. However, when constructing coalition logics about strategic reasoning in special kinds of situations, we may want to keep some of the assumptions. Thus, studying coalition logics with some of these assumptions makes good sense. In this paper, we show the completeness of these coalition logics by a uniform approach.

Problem

• Completeness of coalition logics with specific assumptions
• Addressing overly strong assumptions in strategic reasoning models
• Studying logics with seriality, independence, or determinism properties

Innovation

• Minimal Coalition Logic without assumptions
• Completeness proof for variant logics
• Uniform method for different assumptions